2018/11/28 by Axel Kleinschmidt, Hermann Nicolai, Kleinschmidt, Axel +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.1811.11659
33 pages
arxiv created 2018/11/28 · openalex publication_date 2018/11/28 · arxiv updated 2018/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The representation theory of involutory (or 'maximal compact') subalgebras of infinite-dimensional Kac-Moody algebras is largely terra incognita, especially with regard to fermionic (double-valued) representations. Nevertheless, certain distinguished such representations feature prominently in proposals of possible symmetries underlying M theory, both at the classical and the quantum level. Here we summarise recent efforts to study spinorial representations systematically, most notably for the case of the hyperbolic Kac-Moody algebra E10 where spinors of the involutory subalgebra K(E10) are expected to play a role in describing algebraically the fermionic sector of D=11 supergravity and M theory. Although these results remain very incomplete, they also point towards the beginning of a possible explanation of the fermion structure observed in the Standard Model of Particle Physics.